Global Utilities

Department of Mathematical and Statistical Sciences

Mathematics Staff Members

Dr Alan Andrew
Dr Alan Andrew

Position: Emeritus Scholar
School of Engineering and Mathematical Sciences  
Office location: Room 329, Physical Sciences 2, La Trobe University, Bundoora, VICTORIA 3083.
Office Phone: (03) 9479 1208,
Fax: (03) 9479 2466
Email: A.Andrew@latrobe.edu.au
Publications
  1. A. L. Andrew "Two properties of integers", Math.Gazette 48 (1964), 285-287 (MR 29#4719).
  2. A. L. Andrew, "Higher modes of non-radial oscillations of stars by variational methods", Austral. J. Phys. 20 (1967), 363-368 Phys.Ab.70, 40540.
  3. A. L. Andrew, "A note on the Ritz method with an application to overtone stellar pulsation theory", J. Austral. Math. Soc. 8 (1968), 275-286 (MR 38#2940).
  4. A. L. Andrew, "Non-radial oscillations of massive stars by variational methods", Acad. Roy. Belg. Bull. Cl. Sci.. 5me Ser. 54 (1968), 1046-1055 (Phys. Ab. 73, 2660).
  5. A. L. Andrew, "Application of the Ritz method to non-standard eigenvalue problems", J. Austral. Math. Soc. 10 (1969), 367-384 (MR 41#1204).
  6. A. L. Andrew, "Convergence of approximate operator methods for eigenvectors", Bull. Austral. Math. Soc. 3 (1970), 199-205 (MR 43#1399).
  7. Alan L. Andrew, "Variational solution of some nonlinear eigenvalue problems. I", J. Math. Anal. Appl. 32 (1970), 400-413 (MR 42#4023).
  8. Alan L. Andrew, "Variational solution of some nonlinear eigenvalue problems. II". J. Math. Anal. Appl. 33 (1971), 425-432 (MR 42#4024).
  9. A. L. Andrew and G.C. Elton, "Computation of eigenvectors corresponding to multiple eigenvalues", Bull. Austral. Math. Soc. 4 (1971), 419-422 (MR 43#7050).
  10. Alan L. Andrew, "Variational solution of certain nonlinear eigenvalue problems", Bull. Austral. Math. Soc. 5 (1971), 137-138 (Zbl. 257.65058).
  11. A. L. Andrew, "Solution of equations involving centrosymmetric matrices", Technometrics 15 (1973), 405-407 (Zbl. 261.65027).
  12. Alan L. Andrew, "Eigenvectors of certain matrices", Linear Algebra Appl. 7 (1973), 151-162 (MR 47#6726).
  13. A. L. Andrew, "The mathematics of population growth", Math. Gazette 58 (1974), 272-276 (R.Zh.M. 1975, 7A3).
  14. A. L. Andrew, "Error bounds for the modified Newton's method", Bull. Austral. Math. Soc. 14 (1976), 427-433 (MR 54#11753).
  15. A. L. Andrew, S. A. Morris, G. P. Protomastro and P. J. Stacey, "On mixed partial derivatives", Austral. Math. Soc. Gazette , 4 (1977), 49-54 (MR 57#3335).
  16. Alan L. Andrew, "Convergence of an iterative method for derivatives of eigensystems". J. Computational Phys. 26 (1978), 107-112 (MR 57#11016).
  17. A. L. Andrew, "Existence and uniqueness regions for solutions of nonlinear equations", Bull. Austral. Math. Soc. 19 (1978), 277-282 (MR 80f:47011).
  18. A. L. Andrew, "Iterative computation of derivatives of eigenvalues and eigenvectors", J. Inst. Math. Appl. 24 (1979), 209-218 (MR 80g:65037).
  19. Alan L. Andrew, Frank R. de Hoog and Peter J. Robb, "Leighton's bounds for Sturm-Liouville eigenvalues", J. Math. Anal. Appl. 83 (1981), 11-19 (MR 82k:34022).
  20. Alan L. Andrew, "Computation of higher Sturm-Liouville eigenvalues", Congressus Numerantium 34 (1982), 3-16 (MR 84a:65071).
  21. John W. Paine and Alan L. Andrew, "Bounds and higher-order estimates for Sturm-Liouville eigenvalues", J. Math. Anal. Appl. 96 (1983), 388-394 (MR 85f:34042).
  22. Alan L. Andrew, "Numerical solution of eigenvalue problems for ordinary differential equations", in Computational Techniques and Applications: CTAC-83 (J. Noye, C. Fletcher, eds.), pp.841-852. Amsterdam: North-Holland 1984 (MR 86h:65114).
  23. Alan L. Andrew and John W. Paine, "Correction of Numerov's eigenvalue estimates", Numer. Math. 47 (1985), 289-300 (MR 86j:65101).
  24. A. L. Andrew, "Further comments on 'On the eigenvectors of symmetric Toeplitz matrices' ", IEEE Trans. Acoust. Speech, Signal Processing ASSP-33 (1985), 1013 (MR 87f:94002).
  25. Alan L. Andrew, "Asymptotic correction of finite difference eigenvalues", In Computational Techniques and Applications: CTAC-85 (J. Noye, R. May, eds.) pp.333-341, Amsterdam: North-Holland 1986 (MR 87i:65007).
  26. R. A. S. Fiedler and A. L. Andrew, "Finite element calculations for non-radial oscillations of stars", Austral. J. Phys. 39 (1986), 99-102 (Phys.Ab. 89, 73214).
  27. A. L. Andrew, "The accuracy of Numerov's method for eigenvalues", BIT 26 (1986), 251-253 (MR 87i:65126).
  28. Alan L. Andrew and John W. Paine, "Correction of finite element estimates for Sturm-Liouville eigenvalues", Numer. Math. 50 (1986), 205-215 (MR 88f:65130).
  29. Alan L. Andrew, "Correction of finite element eigenvalues for problems with natural or periodic boundary conditions", BIT 28 (1988), 254-269 (MR 89b:65197).
  30. Alan L. Andrew, "Some recent developments in finite element eigenvalue computation", in Computational Techniques and Applications: CTAC-87 (J. Noye, C. Fletcher, eds.), pp.83-91, Amsterdam: North-Holland 1988 (MR 90f:65142).
  31. Alan L. Andrew, "Efficient computation of higher Sturm-Liouville eigenvalues", Internat. Ser. Numer. Math. (Birkhauser) 86 (1988), 1-9 (MR 90j:65108).
  32. Roger C.E. Tan and Alan L. Andrew, "Computing derivatives of eigenvalues and eigenvectors by simultaneous iteration", IMA J. Numer.Anal. 9 (1989), 111-122 (MR 90h:65067).
  33. Alan L. Andrew, "Correction of finite difference eigenvalues of periodic Sturm-Liouville problems", J. Austral. Math. Soc. (Series B) 30 (1989), 460-469 (MR 89k:65101).
  34. Alan L. Andrew, "Choosing test matrices for numerical software", in Computational Techniques and Applications: CTAC-89 (W.L. Hogarth and B.J. Noye (eds.), pp.561-567, New York: Hemisphere 1990 (MR 92d:00025).
  35. Alan L. Andrew, "Eigenvalues and singular values of certain random matrices", J. Comput. Appl. Math. 30 (1990) 165-171 (MR 91f:65072).
  36. Alan L. Andrew, Frank R. de Hoog and Roger C. E. Tan, "Direct computation of derivatives of eigenvalues and eigenvectors", Internat. J. Computer Math. 36 (1990), 251-255 (Zbl. 709.65030).
  37. Alan L. Andrew and K.-W. Eric Chu, "Comments on `Analytical solutions for the nth derivatives of eigenvalues and eigenvectors for a nonlinear eigenvalue problem'", AIAA J. 29 (1991), 1182-1183 (IAA, A91-45122).
  38. Alan L. Andrew, K.-W. Eric Chu and Peter Lancaster, "Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter", Appl. Math. Lett. 5(3) (1992), 69-72 (MR 93d:15013).
  39. Alan L. Andrew, "Computing two-sided bounds for eigenvalues of differential equations", in Computational Techniques and Applications: CTAC-91 (J. Noye, B. Benjamin and L. Colgan, eds.) pp. 101-108, Adelaide, Comp. Math. Group AMS 1992.
  40. Alan L. Andrew, K.-W. Eric Chu and Peter Lancaster, "Derivatives of eigenvalues and eigenvectors of matrix functions", SIAM J. Matrix Anal. Appl. 14 (1993), 903-926 (MR 94h:65034).
  41. Roger C. E. Tan, Alan L. Andrew and Felicia M. L. Hong "Iterative computation of second-order derivatives of eigenvalues and eigenvectors", Commun. Numer. Meth. Engng. 10 (1994), 1-9 (Zbl. 795.65020).
  42. Alan L. Andrew, "Asymptotic correction of computed eigenvalues of differential equations",Ann. Numer. Math. 1 (1994), 41-51 (MR 96i:65066).
  43. Alan L. Andrew, "Some recent developments in inverse eigenvalue problems" in Computational Techniques and Applications: CTAC-93 (D. Stewart, H. Gardner and D. Singleton, eds) pp. 94-102, Singapore: World Scientific 1994 (Zbl. 872.65001).
  44. Roger C.E. Tan and Alan L. Andrew, "Henrici's transformation and its application to the computation of derivatives of eigensystems", J. Comput. Appl. Math. 59 (1995), 1-8 (MR 96c:65064).
  45. A. L. Andrew, K.-W. E. Chu and P. Lancaster, "On the numerical solution of nonlinear eigenvalue problems" Computing 55 (1995), 91-111 (MR96c:65055).
  46. A. L. Andrew, "Solution of nonlinear and multiparameter eigenvalue problems", in Computational Techniques and Applications: CTAC-95 (R. L. May and A. K. Easton, eds) pp. 97-104, Singapore: World Scientific 1996. (Zbl 909.65028).
  47. Alan L. Andrew and Roger C. E. Tan, "Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration", AIAA J. 34 (1996) 2214-2216 (Zbl 899.65015).
  48. Alan L. Andrew and Roger C. E. Tan, "Computation of derivatives of repeated eigenvalues and the corresponding eigenvectors", Z. Angew. Math. Mech. 76 (Suppl.2) (1996) 467-468. (Zbl 900.65096).
  49. Alan L. Andrew, "Finite and continuous perturbations of matrix eigenvalues", Appl. Math. Lett., 11 (1) (1998), 47-51.
  50. Alan L. Andrew, "Computation of derivatives of eigenvalues and eigenvectors of parameter-dependent matrices", in Computational Techniques and Applications: CTAC-97 (B.J. Noye, M.D. Teubner and A.W. Gill, eds) pp. 51-58, Singapore: World Scientific 1998. (Zbl 980.65043).
  51. Alan L. Andrew, "Iterative methods for computation of derivatives of eigenvalues and eigenvectors". in Proc. 3rd Biennial Engng.Math. Appl. Conf. EMAC'98 (J.A.K. Stott and E.O. Tuck, eds) IE Aust. 1998 (ISBN 185825 686x) pp. 83-86.
  52. Alan L. Andrew, "Centrosymmetric matrices", SIAM Rev., 40 (1998) 697-698, (Zbl 918.15006).
  53. Roger C.E. Tan and Alan L. Andrew, "Computing derivatives of eigenvectors corresponding to multiple eigenvalues of nonsymmetric matrix functions", in Proc. 8th Internat. Colloq. Differential Equations, Plovdiv, Bulgaria 1997 (D. Bainov, ed.) pp. 409-414, Utrecht: VSP 1998. (Zbl 910.65020).
  54. Alan L. Andrew and Roger C.E. Tan, "Computation of derivatives of repeated eigenvalues and the corresponding eigenvectors of symmetric matrix pencils", SIAM J. Matrix Anal. Appl., 20 (1998), 78-100 (MR 99g: 65044).
  55. Alan L. Andrew and Roger C.E. Tan, "Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration", Commun. Numer. Meth. Engng., 15 (1999) 641-649, (Zbl 944.65040).
  56. Alan L. Andrew and Roger C.E. Tan, "Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors", Numer. Linear. Algebra Appl., 7 (2000), 151-167 (MR 2001g: 65036).
  57. Alan L. Andrew, "Quadrature errors in finite element eigenvalue computations", ANZIAM J, 42 (2000), 136 - 140 (Zbl 964.65077).
  58. Alan L. Andrew "Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions", J. Comput. Appl. Math., 125 (2000), 359 - 366 (MR 2001j: 65116).
  59. Alan L. Andrew, "Twenty years of asymptotic correction for eigenvalue computation", ANZIAM J 42(E) (2000) C96-C116 (Zbl 977.65098).
  60. Alan L. Andrew, "Sensitivity problems for multiple eigenvalues in structural analysis", in Proc. 4th Biennial Engng. Math. Appl. Conf. EMAC 2000 (R.L. May, G.F. Fitz-Gerald and I.H. Grundy, eds) 1E Aust 2000 (ISBN 085825705X) pp. 51 - 54.
  61. Alan L. Andrew and Roger C.E. Tan, "Iterative computation of higher derivatives of repeated eigenvalues and the corresponding eigenvectors", Operator Theory: Advances and Applications, 130 (2001) 43-54. (MR 2003c:15009)
  62. Alan L. Andrew, "Asymptotic correction of Numerov's eigenvalue estimates with general boundary conditions", ANZIAM J. 44(E) (2003) C1-C19 (MR 2006f: 65069).
  63. Alan L. Andrew, "Asymptotic correction of more Sturm-Liouville eigenvalue estimates", BIT, 43 (2003) 485-503 (MR 2004m:65104).
  64. Alan L. Andrew, "Numerical solution of inverse Sturm-Liouville problems", ANZIAM J. 45(E) (2004) C326-C337 (Zbl 1063.65551).
  65. Alan L. Andrew, "Numerov's method for inverse Sturm-Liouville problems", Inverse Problems, 21 (2005) 223 - 238 (MR 2006d:65076).
  66. Alan L. Andrew, "Asymptotic correction and inverse eigenvalue problems: an overview", ANZIAM J. 46(E) (2005) C1-C14 (Zbl 1078.65558).
  67. Alan L. Andrew, "Computing Sturm-Liouville potentials from two spectra", Inverse Problems 22 (2006) 2069-2081.
Technical reports (not including preprints of papers submitted for publication)
  1. "Stability scales for use on Tephigrams and adiabatic charts", New Zealand Meteorological Service Tech. Note 137 (1961).
  2. "Eigenvalue problems with nonlinear dependence on the eigenvalue parameter. A bibliography". Tech. Rep., Math. Dept., La Trobe University (1974) (Zbl.313.47007).
  3. (with R.A.S. Fiedler), "Computation of normal modes of non-radial oscillation of stars by the finite element method", Math. Res. Paper 85-4 (1985) La Trobe University.
  4. "Finite difference solution of eigenvalue problems", Math. Res. Paper 90-16 (1990), La Trobe University.
  5. (with R.C.E. Tan), "Some numerical tests of algorithms for computing derivatives of eigenvalues and eigenvectors", Math. Res. Paper 98-23 (1999) La Trobe University.
Minor notes and abstracts of unpublished work.
  1. (with A. Brown), Austral. Math. Teacher 20 (1964), 43-44.
  2. Math. Mag. 45 (1972), 239.
  3. Math. Chronicle 3 (1974), 185.
  4. Austral.Math. Soc. Gazette 2 (1975), 16.
  5. Math. Chronicle 8 (1979), 164-165.
  6. Math. Chronicle 10 (1982), 165.
  7. Math. Chronicle 14 (1985), 101.
  8. (with R. C. E. Tan), in Proc. ICIAM91. 
  9. (with R. C. E. Tan), in Proc. ICIAM95. 
  10. (with R. C. E. Tan), "Application of MATLAB to an eigenvalue problem from mechanical engineering", 6pp., in Proc. First Australian MATLAB Conference, Melbourne, 1996.
Reviews

Over 400 reviews in Mathematical Reviews and Zentralblatt fur Mathematik, as well as book reviews in several other journals including Technometrics and SIAM Review.

 

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Last Updated: 10 March, 2008

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